Capacity peak

If peaks can be adequately distinguished (depending on analytical goals and methods) at some Rs value less than one, then more peaks can be crowded into the separation space and nc increases in accordance with the equation 

If we use a from Eq. 5.54, where we replace migration distance X by L (although LI2 might be better as a mean value), Eq. 5.59 reduces to 

In elution systems like chromatography, nc can be significantly larger than the value indicated in Eq. 5.61 because each successive volume sweeping the column can bring forth and resolve a new group of peaks. Analysis shows that the peak capacity (for adjacent peaks at Rs = 1) is approximately [19] 

The equations of this section show that resolution and peak capacity are inversely proportional to a and w (usually reflected in H and N). These equations illustrate how the capacity for separation is diminished, using any reasonable measure, by increases in zone width. This conclusion reemphasizes our deep concern with zone spreading phenomena and the fundamental transport processes that underlie them. 

The optimal working range in terms of capacity factors will not only be determined by the considerations of analysis time given in the previous section, but also by the number of peaks present in the chromatogram. The theoretical peak capacity (np of a chromatogram can be found from [104] 

Davis and Giddings [105] have argued that the theoretical peak capacity is usually not even approached. Instead, they conclude that in order to provide a 90% probability for a compound of interest to appear as a pure peak in the chromatogram, the available peak capacity should exceed the theoretically required value (eqn.1.25) by a factor of 20. If we consider the same range of capacity factors this results in an excess plate count of about a factor of 400. 

In the treatment of Davis and Giddings the peaks are supposed to be randomly distributed over the chromatogram. Optimization of selectivity can be seen as the process to fight statistics and to approach the theoretical peak capacity as closely as possible. 

Although relatively unknown, the instrumentation for 2DLC was conceived and implemented by Emi and Frei (1978). They reported the valve configuration presently used in most comprehensive 2DLC systems. However, they automated neither the valve nor the data conversion process to obtain a contour map or 2D peak display. They used a gel permeation chromatography (GPC) column in the first dimension and a reversed-phase liquid chromatography (RPLC) column in the second dimension and studied complex plant extracts. 

It is this ordering that gave the concept a theoretical bent as real separations are not ordered the retention times in most separation techniques appear almost random across a range of separation time. The mathematical definition of peak capacity, nc, for an isocratic separation is given as (Grushka, 1970) 

Constant peak width is recognized to give more peak capacity in LC and the same is true in 2DLC. The use of this equation is interesting in that the number of theoretical plates is not constant across a chromatogram of constant peak width. This is easily shown by recalling the definition of the number of plates as 

As discussed below, if the two media used for separation in 2DLC are correlated with respect to the retention mechanism, the peak capacity will be lower than expected from the product approximation. The dependence of the peak capacity product on the correlation between retention mechanisms is covered in Chapter 3. Furthermore, as pointed out by Carr and coworkers (Stoll et al., 2006), if the second dimension sampling of the first dimension is undersampled, the potential peak capacity will not be able to be utilized. This is discussed in the theory of zone sampling section below. Further implications of peak capacity limitations due to sampling have been recently given by Tanaka and coworkers (Horie et al., 2007). 

There has been an attempt to measure the peak capacity in 1DLC and 2DLC by assigning a range of useful retention time between the unretained marker that elutes at ti and some stated value of the retention factor k leading to a zone at tf and plugging in a value for the peak width W. This number is useful but will never be equal to the number 

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Another important consideration is the number of solutes that can be baseline resolved on a given column. An estimate of a column s peak capacity, is... 

To minimize the multiple path and mass transfer contributions to plate height (equations 12.23 and 12.26), the packing material should be of as small a diameter as is practical and loaded with a thin film of stationary phase (equation 12.25). Compared with capillary columns, which are discussed in the next section, packed columns can handle larger amounts of sample. Samples of 0.1-10 )J,L are routinely analyzed with a packed column. Column efficiencies are typically several hundred to 2000 plates/m, providing columns with 3000-10,000 theoretical plates. Assuming Wiax/Wiin is approximately 50, a packed column with 10,000 theoretical plates has a peak capacity (equation 12.18) of... 

Kovat s retention index (p. 575) liquid-solid adsorption chromatography (p. 590) longitudinal diffusion (p. 560) loop injector (p. 584) mass spectrum (p. 571) mass transfer (p. 561) micellar electrokinetic capillary chromatography (p. 606) micelle (p. 606) mobile phase (p. 546) normal-phase chromatography (p. 580) on-column injection (p. 568) open tubular column (p. 564) packed column (p. 564) peak capacity (p. 554)... 

A more recent discussion of peak capacity is presented in the following paper. 

The peak capacity of a column has been defined as the number of peaks that can be fitted into a chromatogram between the dead point and the last peak, with each peak being separated from its neighbor by 4a. The last peak of chromatogram is rather a... 

Peak capacity can be very effectively improved by using temperature programming in GC or gradient elution in LC. However, if the mixture is very complex with a large number of individual solutes, then the same problem will often arise even under programming conditions. These difficulties arise as a direct result of the limited peak capacity of the column. It follows that it would be useful to derive an equation that... 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

However, with practical samples the way the (k ) values of the individual components for any given complex solute mixture are distributed is not predictable, and will vary very significantly from mixture to mixture, depending on the nature of the sample. Nevertheless, although the values for the theoretical peak capacity of a column given by equation (26) can be used as a reasonable practical guide for comparing different columns, the theoretical values that are obtained will always be in excess of the peak capacities that are actually realized in practice. 

It is also apparent from Figure 20 that any property of the chromatographic system that places a limit on the maximum value of (k ) must also limit the maximum peak capacity that is attainable. One property of the system that limits the maximum value... 

Figure 20. Graph of Peak Capacity against Capacity Ratio...

Equation (33) shows that the maximum capacity ratio of the last eluted solute is inversely proportional to the detector sensitivity or minimum detectable concentration. Consequently, it is the detector sensitivity that determines the maximum peak capacity attainable from the column. Using equation (33), the peak capacity was calculated for three different detector sensitivities for a column having an efficiency of 10,000 theoretical plates, a dead volume of 6.7 ml and a sample concentration of l%v/v. The results are shown in Table 1, and it is seen that the limiting peak capacity is fairly large. 

Table 1. Capacity Ratios and Peak Capacities for Detectors of...

Detector Sensitivity Maximum (k ) Retention Time (min.) Peak Capacity... 

The analytical capability of a SEC column is sometimes judged by the peak capacity, which is the number of unique species that can be resolved on any given SEC column. This number will increase with decreased particle size, increased column length, and increased pore volume. Because small particlesized medium generally has a lower pore volume and a shorter column length, peak capacities of ca. 13 for fully resolved peaks can be expected for high-resolution modern media as well as traditional media, (see Eig. 2.5). It was found that SEC columns differ widely in pore volume, which affects the effective peak capacity (Hagel, 1992). 

FIGURE 2.5 Theoretical peak capacity of different columns for SEC. 

One final quality parameter that is sometimes specified in test methods is the peak capacity of the column set. In the literature of the OECD, this peak capacity is required to have a value of 6.0 or greater. This peak capacity is defined by Eq. (2) ... 

The peak capacity, n, of a single-column chromatographic system generating N theoretical plates is given by ... 

The limitations of one-dimensional (ID) chromatography in the analysis of complex mixtures are even more evident if a statistical method of overlap (SMO) is applied. The work of Davis and Giddings (26), and of Guiochon and co-workers (27), recently summarized by Jorgenson and co-workers (28) and Bertsch (29), showed how peak capacity is only the maximum number of mixture constituents which a chromatographic system may resolve. Because the peaks will be randomly rather than evenly distributed, it is inevitable that some will overlap. In fact, an SMO approach can be used to show how the number of resolved simple peaks (5) is related to n and the actual number of components in the mixture (m) by the following ... 

Table 1.4 Peak capacities in modem high-resolution cliromatography ...

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